Both sentences are correct and convey the same basic idea, but they have slightly different structures.
"I take her to and from school every day."
This sentence is concise and indicates that you are responsible for both taking her to school and bringing her back from school every day.
"I take her to school and pick her up from school every day."
This sentence is more explicit and provides additional detail by separating the actions of taking her to school and picking her up from school. It emphasizes both parts of the daily routine.
Both sentences are grammatically sound and convey the same essential meaning. The choice between them depends on the level of detail and emphasis you want to include in your statement.